Why I cannot subdivide face in this way?
When you subdivide this way, you're not subdividing a face, just one of it's edges.  Joining the new vertices up later with F still won't subdivide the original face.  

Have you tried selecting both edges together, then doing the subdivide?  This should split the face up into two. 

Select one edge, hold SHIFT down and select the other.
With both edges highlited, press W and do the subdivide.